The following results are obtained through intensive discussions and collaboration with Prof. Michel Loreau, researchers at Ecole Normale superieure and Center for Population Biology, Imperial College, Silwood Park.1) As a biodiversity effect at a large spatial scale, spatial population structure like meta community, the responses of which do not synchronize against environmental fluctuation, can enhance the stability of ecosystem functioning like "insurance hypothesis" in the long-term (Loreau, M., Mouquet, N. & Gonzalez, A. (2003)).2) While alpha diversity of an ecosystem maintains its ecosystem functioning at a spatially smaller scale, beta diversity can be expected to tune the spatial structure of alpha diversity of each ecosystem according to a spatially heterogeneous environmental gradient, thus expected to enhance the ecosystem functioning at a larger spatial scale.3) The importance of making clear the relationships between biodiversity and its effects at' each temporal & spatial scale by filling them in a spatio-temporal matrix was agreed.4) According to 3), biodiversity effect at a smaller spatial scale and shorter temporal scale was examined theoretically. We analyzed a model to evaluate the complementarity effect and the selection effect. Based on the results, we compared with the statistical method which deals with the experimental data (manuscript in preparation).